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An improved upper bound for the error in the zero-counting formulae for Dirichlet $ L$-functions and Dedekind zeta-functions


Author: T. S. Trudgian
Journal: Math. Comp. 84 (2015), 1439-1450
MSC (2010): Primary 11M06; Secondary 11M26, 11R42
DOI: https://doi.org/10.1090/S0025-5718-2014-02898-6
Published electronically: September 15, 2014
MathSciNet review: 3315515
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Abstract: This paper contains new explicit upper bounds for the number of zeroes of Dirichlet $ L$-functions and Dedekind zeta-functions in rectangles.


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Additional Information

T. S. Trudgian
Affiliation: Mathematical Sciences Institute, The Australian National University, Canberra, Australia, 0200
Email: timothy.trudgian@anu.edu.au

DOI: https://doi.org/10.1090/S0025-5718-2014-02898-6
Keywords: Zero-counting formula, Dirichlet $L$-functions, Dedekind zeta-functions
Received by editor(s): June 8, 2012
Received by editor(s) in revised form: November 7, 2012, April 16, 2013, and August 12, 2013
Published electronically: September 15, 2014
Additional Notes: Supported by Australian Research Council DECRA Grant DE120100173.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.